In a general sense, imperium was the scope of someone's power, and could include anything, such as public office, commerce, political influence, or wealth.
Imperium originally meant absolute or kingly power—the word being derived from the Latin verb imperare (to command)—which became somewhat limited under the Republic by the collegiality of the republican magistrates and the right of appeal, or provocatio, on the part of citizens.
[1][2] In ancient Rome, imperium could be used as a term indicating a characteristic of people, their wealth in property, or the measure of formal power they had.
When in the field, a curule magistrate possessing an imperium greater or equal to that of a praetor wore a sash ritually knotted on the front of his cuirass.
The first pope who used it in an official act and relied upon it, Leo IX, cites the "Donatio" in a letter of 1054 to Michael Cærularius, Patriarch of Constantinople, to show that the Holy See possessed both an earthly and a heavenly imperium, the royal priesthood.
Thenceforth, the "Donatio" acquires more importance and is more frequently used as evidence in the ecclesiastical and political conflicts between the papacy and the secular power: Anselm of Lucca and Cardinal Deusdedit inserted it in their collections of canons; Gratian excluded it from his Decretum, but it was soon added to it as Palea; the ecclesiastical writers in defence of the papacy during the conflicts of the early part of the 12th century quoted it as authoritative.
In one bitter episode, Pope Gregory IX, who had several times mediated between the Lombards and the Holy Roman Emperor Frederick II, reasserted his right to arbitrate between the contending parties.
The pope again excommunicated the "self-confessed heretic", the "blasphemous beast of the Apocalypse" (20 March 1239) who now attempted to conquer the rest of Italy (i.e., the papal states, et cetera).